Advancements in Quantum Computing (QC) and Neural Combinatorial Optimization (NCO) represent promising steps in tackling complex computational challenges. On the one hand, Variational Quantum Algorithms such as QAOA can be used to solve a wide range of combinatorial optimization problems. On the other hand, the same class of problems can be solved by NCO, a method that has shown promising results, particularly since the introduction of Graph Neural Networks. Given recent advances in both research areas, we introduce Hamiltonian-based Quantum Reinforcement Learning (QRL), an approach at the intersection of QC and NCO. We model our ansatzes directly on the combinatorial optimization problem's Hamiltonian formulation, which allows us to apply our approach to a broad class of problems. Our ansatzes show favourable trainability properties when compared to the hardware efficient ansatzes, while also not being limited to graph-based problems, unlike previous approaches. In this work, we evaluate the performance of Hamiltonian-based QRL on a diverse set of combinatorial optimization problems to demonstrate the broad applicability of our approach and compare it to QAOA.Advancements in Quantum Computing (QC) and Neural Combinatorial Optimization (NCO) represent promising steps in tackling complex computational challenges. On the one hand, Variational Quantum Algorithms such as QAOA can be used to solve a wide range of combinatorial optimization problems. On the other hand, the same class of problems can be solved by NCO, a method that has shown promising results, particularly since the introduction of Graph Neural Networks. Given recent advances in both research areas, we introduce Hamiltonian-based Quantum Reinforcement Learning (QRL), an approach at the intersection of QC and NCO. We model our ansatzes directly on the combinatorial optimization problem's Hamiltonian formulation, which allows us to apply our approach to a broad class of problems. Our ansatzes show favourable trainability properties when compared to the hardware efficient ansatzes, while also not being limited to graph-based problems, unlike previous approaches. In this work, we evaluate the performance of Hamiltonian-based QRL on a diverse set of combinatorial optimization problems to demonstrate the broad applicability of our approach and compare it to QAOA.

arXiv:2405.07790IEEE International Conference on Quantum Computing and Engineering (QCE)Sep 15, 20244 citations

Solving Combinatorial Optimization Problems on a Photonic Quantum Computer

Mateusz Slysz, Krzysztof Kurowski, Grzegorz Waligóra

Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration into alternative paradigms such as quantum computing. In this paper, we investigate the application of photonic quantum computing to solve combinatorial optimization problems. Leveraging the principles of quantum mechanics, we demonstrate how photonic quantum computers can efficiently explore solution spaces and identify optimal solutions for a range of combinatorial problems. We provide an overview of quantum algorithms tailored for combinatorial optimization for different quantum architectures (boson sampling, quantum annealing and gate-based quantum computing). Additionally, we discuss the advantages and challenges of implementing those algorithms on photonic quantum hardware. Through experiments run on an 8-qumode photonic quantum device, as well as numerical simulations, we evaluate the performance of photonic quantum computers in solving representative combinatorial optimization problems, such as the Max-Cut problem and the Job Shop Scheduling Problem.Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration into alternative paradigms such as quantum computing. In this paper, we investigate the application of photonic quantum computing to solve combinatorial optimization problems. Leveraging the principles of quantum mechanics, we demonstrate how photonic quantum computers can efficiently explore solution spaces and identify optimal solutions for a range of combinatorial problems. We provide an overview of quantum algorithms tailored for combinatorial optimization for different quantum architectures (boson sampling, quantum annealing and gate-based quantum computing). Additionally, we discuss the advantages and challenges of implementing those algorithms on photonic quantum hardware. Through experiments run on an 8-qumode photonic quantum device, as well as numerical simulations, we evaluate the performance of photonic quantum computers in solving representative combinatorial optimization problems, such as the Max-Cut problem and the Job Shop Scheduling Problem.

arXiv:2409.13781Sep 19, 20241 citation

Characterizing QUBO Reformulations of the Max-k-Cut Problem for Quantum Computing

Adrian Harkness, Hamidreza Validi, Ramin Fakhimi +4 more

Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a quadratic unconstrained binary optimization (QUBO) problem. The solution of the QUBO reformulation can then be addressed using adiabatic quantum computing devices or appropriate quantum computing algorithms on gate-based quantum computing devices. In general, QUBO reformulations of combinatorial problems can be readily obtained by properly penalizing the violation of the problem's constraints in the original problem's objective. However, characterizing tight (i.e., minimal but sufficient) penalty coefficients for this purpose is important and non-trivial for enabling the solution of the resulting QUBO in current and near-term quantum computing devices. Along these lines, we present closed-form characterizations of tight penalty coefficients for two distinct QUBO reformulations of the max $k$ -cut problem whose values depend on the (weighted) degree of the vertices of the graph defining the problem. These findings contribute to the ongoing effort to make quantum computing a viable tool for solving combinatorial problems at scale. We support our theoretical results with illustrative examples and simple numerical results.Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a quadratic unconstrained binary optimization (QUBO) problem. The solution of the QUBO reformulation can then be addressed using adiabatic quantum computing devices or appropriate quantum computing algorithms on gate-based quantum computing devices. In general, QUBO reformulations of combinatorial problems can be readily obtained by properly penalizing the violation of the problem's constraints in the original problem's objective. However, characterizing tight (i.e., minimal but sufficient) penalty coefficients for this purpose is important and non-trivial for enabling the solution of the resulting QUBO in current and near-term quantum computing devices. Along these lines, we present closed-form characterizations of tight penalty coefficients for two distinct QUBO reformulations of the max $k$-cut problem whose values depend on the (weighted) degree of the vertices of the graph defining the problem. These findings contribute to the ongoing effort to make quantum computing a viable tool for solving combinatorial problems at scale. We support our theoretical results with illustrative examples and simple numerical results.

quant-pharXiv:2511.01108Nov 4, 20250 citations

Some mathematical results in quantum computation

Qiujie Sun

Journal of Southwest UniversityJan 1, 20050 citations

k

-cut problem whose values depend on the (weighted) degree of the vertices of the graph defining the problem. These findings contribute to the ongoing effort to make quantum computing a viable tool for solving combinatorial problems at scale. We support our theoretical results with illustrative examples and simple numerical results.